Shrunken People

Suppose someone is shrunken by some gimmick in the movies. Let’s say that you suffer this consequence and are now 100 times smaller in all dimensions. Actually, there is a lot of space between the atoms and molecules of our bodies, but let’s ignore any increase in repulsive forces, etc., and assume that this shrinkage can be done. What does physics tell you will be a major problem as you walk?

Answer

We assume that the proposed shrinking to one-hundredth scale can be accomplished. Unfortunately, your weight would remain the same (unless you get rid of molecules somehow), and your density would increase a million fold! The area of contact of your feet would be 10,000 times smaller, so the pressure at your soles would be 10,000 times greater, rising to about 20,000 psi. Every step would break the concrete, or you would sink into the ground until the upward normal force could balance you. Among other changes, your metabolism must change enormously, for your high ratio of surface area to volume will mean that the rate of heat loss has increased at least 100 times. Of course, we choose to ignore any consequences inside the body for simplicity.

Notice that if the opposite happens and you grow bigger and increase your size by a factor of 100 in all directions, without adding molecules, your density decreases a million fold. You would be blown away by practically any breeze! But your greater problem would be that your density is now much less than the density of air, so the buoyant force upward would be greater than your weight. You are now a giant balloon being pushed upward toward the upper atmosphere! Also, your metabolism would change dramatically, but again, we ignore any consequences inside your body. You could probably make the journey around the world in 80 days without the hot air!